The background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
Web-based graphing calculator programs for general use that run on a browser and web-based graphing calculator programs optimized for mobile devices such as smartphones and tablets are rapidly increasing in popularity. Such devices are a convenient substitute to carrying a separate specialized graphing calculator (such as the TI-83 Plus or TI-84 Plus or other ubiquitous TI graphing calculators) for students, engineering professionals and others who need to use such a portable device in their daily activities on worksites or in campus classrooms.
Accessibility for visually and hearing-impaired persons to such computing and mathematical applications and devices has long been an area of ongoing research. One challenging research area is finding ways to express graphical output such as curves on a Cartesian, polar or other coordinate system in a comprehensible manner for persons who are blind or low vision. Verbal output systems function well for persons relying on screen reader technology to voice computer activity. A screen reader is software that runs on computer systems which converts text on screen into spoken or Braille output to enable persons who are blind or low vision to operate a computer system. For example, “start fraction, 1 over 2, end fraction” is a reasonable syntax to verbally describe a fraction. However, for following more complex mathematical expressions, verbal output may be more complicated to follow. In addition, hearing and/or visually impaired students who are Braille readers may find verbal output systems inadequate. People who rely on Braille for communication use well-established codes for communicating arithmetic ideas that may be used to adapt calculator functions to Braille input and output devices.
According to the Random House Dictionary, Braille is “a system of writing and printing for the blind in which arrangements of raised dots representing letters and numbers can be identified by touch.” Each Braille character, known as a cell, consists of a combination of six or eight dots, The Braille code is used by people who are low vision or totally blind to read and write, typically with manual writing devices such as the Perkins Brailler, a slate and stylus, specialized embossers, or electronic displays which can operate stand-alone or serve as input and output terminals when connected to computers. More information about Braille is available at https://en.wikipedia.org/wiki/Braille. In addition to literary contexts, codes specific to the domains of math, science and music notation (which, like their print and typeset counterparts to literary text, bear little resemblance to literary Braille) have been developed over time. Common mathematical Braille codes include Nemeth, Unified English Braille (UEB), Computer Braille and UNICODE Braille.
Existing Braille translation systems are designed to translate primarily literary works, and in some limited cases mathematical works, but only as part of desktop software (such as the Duxbury Braille Translator or as part of screen reading programs such as JAWS for Windows and Apple's VoiceOver for the Mac and iOS platforms). There are few, if any, math-to-Braille libraries that exist for use in an online context that translate common mathematical coding formats such as LaTeX to common mathematical Braille codes. One other commonly known online Braille math input system, Pearson's Accessible Equation Editor (http://accessibility.pearson.com/aee), translates only a modified Nemeth syntax to MathML, and is unable to translate LaTeX into Nemeth and UEB, and cannot supply both equations and their answers in the user's preferred Braille code.
The Nemeth Braille code, developed by Dr. Alexander Nemeth, has been the standard set of rules and symbols for describing mathematics in the United States since 1972. It details comprehensive rules to describe many facets of math, including algebra, geometry, trigonometry, calculus and logic. The reference document (see link below) also includes numerous examples of mathematical expressions that have been incorporated in embodiments of the present invention to ensure accurate translation to and from LaTeX in the calculator of the present invention. While it is broadly known, Nemeth Braille code is used primarily in the United States and Canada. See Nemeth overview on Wikipedia (https://en.wikipedia.org/wiki/Nemeth_Braille) and The Nemeth Braille Code for Mathematics and Scientific Notation 1972 (https://nfb.org/images/nfb/documents/pdf/nemeth_1972.pdf)
For decades, English-speaking countries, such as the United States, Great Britain and Australia have written and maintained separate literary and scientific Braille codes. Though the literary specifications differ superficially from one another, the scientific notations are vastly dissimilar. As the electronic interchange of Braille documents has grown in popularity, blindness organizations in the above countries recognized a need to create an internationally recognized standard for creating distributing these files across national boundaries.
Unified English Braille, referred to hereinafter as UEB, was the result of many years' effort. It seeks to create a one-to-one mapping of all literary and scientific symbols to Braille dot patterns (which may encompass one or more cells). UEB is relatively new in comparison to older, more established codes, such as the previous United States literary and Nemeth math systems), and as a result there is much less documentation available aside from the official UEB technical guidelines. Also, while UEB became the standard for literary Braille in the United States in January 2016, it has been left for individual states to decide which system to use for technical material. Anecdotal research has shown that at the time of writing, Nemeth has much broader support than UEB. See UEB overview available at https://en.wikipedia.org/wiki/Unified_English_Braille and UEB Guidelines for Technical Material at http://www.brailleauthority.org/ueb/Guidelines_for_Technical_Material_2008-10.pdf.
Another form of Braille encoding, Computer Braille, defines an exact 1-to-1 relationship between the standard ASCII character set and a single Braille cell. It is what an end user reads and writes when his or her Braille device operates without an active translator, and it is the only mode of input and output available on every Braille device manufactured throughout the world. While it has been superseded by UEB as an official standard in many countries Computer Braille's uniform implementation across all modern electronic Braille devices makes it ideal for unambiguous input and output. See Overview of Computer Braille available at: https://en.wikipedia.org/wiki/Computer_Braille_Code and Computer Braille reference at http://www.brailleauthority.org/cbc/cbc2000.pdf.
The UNICODE Braille standard defines a block of characters, called “Braille Patterns,” in the range U+2800 through U+28FF. The patterns comprise all possible 64 combinations of six dot Braille characters. See UNICODE Braille Patterns Overview at https://en.wikipedia.org/wiki/Braille_Patterns.